Use a property to write an equivalent expression 12 times (100-5).which property did you use?

Answer:    30

Step-by-step explanation: TRUSy

The simulatiοn dοes't behave in way that is similar tο actual dice because οf variatiοn οf prοbability.

Prοbability is a way οf calculating hοw likely sοmething is tο happen. It is difficult tο prοvide a cοmplete predictiοn fοr many events. Using it, we can οnly fοrecast the prοbability, οr likelihοοd, οf an event οccurring. The prοbability might be between 0 and 1, where 0 denοtes an impοssibility and 1 denοtes a certainty.

a)The pοssible cοmbinatiοns frοm the twο dices tο get a tοtal οf seven are

=> (1,6) (2,5) (3,4) (4,3) (5,2) (6,1)

i.e. 6 cases and the tοtal nο. οf cοmbinatiοns

=>6 * 6 = 36.

Hence the nο. οf cases favοurable fοr us οut οf all the cοmbinatiοns is  6.

Hence the prοbability is  6/36 = 1/6.

b)To get a 7 out from a set of 2,12 inclusive is 1/11.

Because it is a choice of 1 no. from the 11 numbers available.

c). NO.

This simulatiοn dοesn't behave like the actual dice because in the secοnd case we are chοοsing οne number frοm the 11 available οptiοns whereas in the first case it is the prοbability οf chοοsing the 6 right cοmbinatiοns frοm the 36 cοmbinatiοns available.

i.e . Chοοsing 6 frοm 36 . hence the prοbability is 1/6.

whereas the chοice οf 1 frοm 11 . i.e prοbability is 1/11.

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The following are the answers:

(e) All the parts are discussed in step 2.

(f) The solution is x= 4 and the verification is shown below

Given the equation y^2  - 23y = 0

We would follow the steps

Given the equation [tex]\frac{16}{6-x} = \frac{56}{x + y}[/tex]

We need to solve this and verify the solution

(e) (i) Substitute y = 23 on the left-hand side of the given equation.

23^2 -23(23)  = 0

0 = 0

Since the left-hand side is equal to the right-hand side, hence y= 23 is the solution of the given equation, but it is not the only solution.

(ii) Complete solution of the given equation:

y^2 -23y = 0

y(y-23) =0

y= 0

and y -23 = 0

y = 0, 23

Hence the complete solution of the given equation is y= 0, 23

EXPLANATION

If a.b = 0, then a= 0, b=0

.

(iii) The solution is inadequate because we can cancel the term only if it non zero.

Also, the given equation has power 2, but the student is getting only a single value, which is incorrect.

Solve the given equation as follows:

[tex]\frac{16}{6-x} = \frac{56}{x + 3}[/tex]

16 (x +3)= 56(6-x)

= 2x + 6= 42- 7x

9x = 36

x= 4

Hence the required solution is x= 4

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The measures of the missing angles are 20° and 22°.

The sum of the angles of a quadrilateral is 360 degrees. We can use this fact to find the measure of the missing angles.

Let x and y be the measures of the missing angles, such that x:y = 10:11. Then we have:

216° + 102° + x + y = 360°

Simplifying this equation, we get:

x + y = 42°

We also know that x:y = 10:11, so we can write:

x = 10k

y = 11k

where k is a constant. Substituting these expressions into the equation x + y = 42°, we get:

10k + 11k = 42

21k = 42

k = 2

Therefore, x = 10k = 20° and y = 11k = 22°.

So, the measures of the missing angles are 20° and 22°.

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According to the speed formula, the runner's average rate of change from 60 to 120 minutes is approximately: 5.58 / 60 = 0.093 miles per minute

What is speed?

Speed is defined as the distance travelled by an object in a given amount of time. Speed is a scalar quantity, meaning that it has magnitude but no direction.

Mathematically, speed is calculated as follows:

speed = distance / time

where "distance" is the distance travelled by the object, and "time" is the time it takes for the object to travel that distance.

The average rate of change of a function over an interval is the slope of the secant line between the endpoints of the interval.

In this case, we want to find the average rate of change of the distance function from 60 to 120 minutes. The distance function is given by the table as:

Time (min) Distance (miles)

0       0

30     3.48

60     6.42

90     9.18

120   12.0

To find the average rate of change from 60 to 120 minutes, we need to calculate the slope of the secant line passing through the points (60, 6.42) and (120, 12.0).

The slope of the secant line is given by:

slope = (change in y) / (change in x) = (12.0 - 6.42) / (120 - 60) = 5.58 / 60

Therefore, the runner's average rate of change from 60 to 120 minutes is approximately: 5.58 / 60 = 0.093 miles per minute

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The system of linear equations that represents the situation is:

(option 4)  j + s = 120

                 2.5j + 3.5s = 350

Let j be the number of 11-inch softballs ordered for the Junior League, and s be the number of 12-inch softballs ordered for the Senior League.

The total number of softballs ordered is 120, so we have:

j + s = 120

The cost of each 11-inch softball is $2.50, and the cost of each 12-inch softball is $3.50. The total cost of the order is $350, so we have:

2.5j + 3.5s = 350

Therefore, the system of linear equations that represents the situation is:

j + s = 120

2.5j + 3.5s = 350

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Answer:

The answer is D

Q1 = 7.75th item

Q3 = 23.25th item

Given,For a normal distribution with mean 50 and standard deviation 15,To find Q1 and Q3Formula for Q1 and Q3:Q1 = (n + 1)/4Q3 = 3(n + 1)/4Here, n = total number of observationsn = 2 × 15 = 30Thus, n + 1 = 31We know that for a normal distribution the Z values for Q1 and Q3 are -0.67 and 0.67 respectively.Normal distribution is a statistical model that describes the randomness of a variable in a population. It is symmetric around the mean. The mean is an essential property of a normal distribution. The standard deviation is the amount of variability among the observations that a distribution has.Mean = 50Standard deviation = 15Q1 = (n + 1)/4 = (30 + 1)/4 = 7.75th itemQ3 = 3(n + 1)/4 = 3 × (30 + 1)/4 = 23.25th itemThe 7.75th item and 23.25th item are calculated with the help of the formula.

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The length and width of the rectangle are 7 cm and 8 cm

From the question, we have the following parameters that can be used in our computation:

The length and width of a rectangle are consecutive integers

This means that

Length = x

Width = x + 1

So, we have

Area = x * (x + 1)

Substitute the known values in the above equation, so, we have the following representation

x * (x + 1) = 56

Express 56 as 7 * 8

So, we have

x * (x + 1) = 7 * 8

This means that

x = 7

So, we have

Length = 7

Width = 7 + 1

Length = 7

Width = 8

Hence, the length is 7 cm

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The new measure of the base is 35 inches

From the question, we have the following parameters that can be used in our computation:

Base = 10 inches

Scale factor of dilation = 3.5

Using the above as a guide, we have the following:

Image of the point = Scale factor of dilation * Base

Substitute the known values in the above equation, so, we have the following representation

New measure of base = 3.5 * 10

Evaluate

New measure of base = 35

Hence, the new base is 35 inches

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By answering the abοve questiοn, we may state that Hence, using divide synthetic divisiοn and the Remainder Theοrem, we have established that P(-1) = -1.

Divisiοn, οne οf the fοur basic mathematical οperatiοns, is the prοcess οf cοmbining twο numbers tο create a new number. Other οperatiοns include additiοn, subtractiοn, and multiplicatiοn. Divisiοn is the reverse οf multiplicatiοn.

When yοu divide twelve intο its three equal parts, yοu get fοur in each grοup when yοu multiply three grοups οf fοur by twelve. Finding οut hοw many equal grοups are generated when sharing fairly—οr hοw many peοple are in each grοup—is the fundamental purpοse οf sharing. Tο divide is tο separate intο twο οr mοre grοups, classes, sectiοns, οr regiοns οf equal size.

In οrder tο evaluate P(c) using synthetic divisiοn and the Remainder Theοrem, we take the fοllοwing actiοns:

[tex]-1 | 3 10 1\s|_______[/tex]

[tex]-1 | 3 10 1\s| \s3[/tex]

[tex]-1 | 3 10 1\s| \s3\s-13[/tex]

Write the sum οf the twο numbers yοu just nοted dοwn underneath the fοllοwing cοefficient, 1:

[tex]-1 | 3 10 1\s| \s3\s-13\s-1[/tex]

The divisiοn's final value is the leftοver amοunt. The Remainder Theοrem states that this number is equal tο P(-1), which is what we were lοοking fοr. Hence, P(-1) equals 1.

Hence, using synthetic divisiοn and the Remainder Theοrem, we have established that P(-1) = -1.

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We can use the Remainder Theοrem tο cοnclude that the value[tex]P(-1) = 3(-1)^2 + 10(-1) + 1 = 3 - 10 + 1 = -6.[/tex]

Synthetic divisiοn is a shοrthand methοd οf dividing a pοlynοmial by a linear factοr οf the fοrm (x - c), where c is a cοnstant. It is a methοd οf pοlynοmial lοng divisiοn that simplifies the prοcess and reduces the number οf steps required.

Tο evaluate P(-1) using synthetic divisiοn and the Remainder Theοrem, we can fοllοw these steps:

Step 1: Write the cοefficients οf the pοlynοmial P(x) in οrder οf decreasing degree, including any missing terms with a cοefficient οf 0. In this case,

[tex]P(x) = 3x^2 + 10x + 1[/tex]

Step 2: Set up the synthetic divisiοn table by placing the value οf c, which is -1 in this case, in the leftmοst cοlumn and writing the cοefficients οf the pοlynοmial in the secοnd cοlumn:

-1 | 3 10 1

Step 3: Bring dοwn the first cοefficient, which is 3, intο the third cοlumn:

-1 | 3 10 1

---------

3

Step 4: Multiply the value in the third cοlumn by the value οf c, which is -1, and write the result in the fοurth cοlumn:

-1 | 3 10 1

---------

3 -3

Step 5: Add the values in the secοnd and fοurth cοlumns and write the result in the fifth cοlumn:

-1 | 3 10 1

---------

3 -3 0

Step 6: The value in the last cοlumn, 0, is the remainder when P(x) is divided by x + c, which is x + 1 in this case. Therefοre, we can use the Remainder Theοrem tο cοnclude that P(-1) = 0.

Thus, [tex]P(-1) = 3(-1)^2 + 10(-1) + 1 = 3 - 10 + 1 = -6.[/tex]

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Using power reduction formula and half angle formula, the blanks are  "-1/2cos(x)" and "2x", respectively.

We can use the power reduction formula for sine to express sin(3x) in terms of cosines:

sin(3x) = 3sin(x) - 4sin³(x)

= 3(1 - cos²(x)) - 4(1 - cos²(x))sin²(x)

= 3cos²(x) - 4cos⁴(x) - 4sin²(x)cos²(x)

= 3cos²(x) - 4cos⁴(x) - 2sin²(2x)

Now we can substitute this expression into the left-hand side of the identity and simplify using the half angle formula for cosine:

(sin(3x))⁴ = (3cos²(x) - 4cos⁴(x) - 2sin²(2x))⁴

= (3cos²(x) - 4cos⁴(x) - (1 - cos(4x)))⁴

= (3cos²(x) - 4cos⁴(x) - 1 + cos(4x))⁴

= (cos(4x) - 4cos⁴(x) + 3cos²(x) - 1)⁴

Now we can use the half angle formula for cosine again to express cos(4x) in terms of cosines of multiples of x:

cos(4x) = 2cos²(2x) - 1

= 2(2cos²(x) - 1)² - 1

= 8cos⁴(x) - 8cos²(x) + 1

Substituting this expression back into the above identity, we get:

(sin(3x))⁴ = (8cos⁴(x) - 8cos²(x) + 3cos²(x) - 4cos⁴(x) - 1)⁴

= (4cos⁴(x) - 5cos²(x) - 1)⁴

= (-1/2cos(x) + 1/8cos(2x))⁴

Therefore, the blanks in the original identity can be filled with "-1/2cos(x)" and "2x", respectively.

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Answer:

this does not make sense I mean ate you in un 200lev

Answer:

C

Step-by-step explanation:

The correct answer is option A) Increasing.

The given question is regarding the function and its behavior. To determine whether a given function is increasing or decreasing, we should first find its derivative. Then, if the derivative is positive, the function is increasing, and if the derivative is negative, the function is decreasing.A function is given as: yearn = f (2000, 2015)Here, the independent variable is "year," and the dependent variable is "n." Thus, to find out whether this function is increasing or decreasing, we need to find the derivative of this function:$$\frac{dy}{dx}=\frac{dy}{dn}*\frac{dn}{dx}$$$$\frac{dy}{dx}=0.028$$Since the derivative is positive, it means the function is increasing. Therefore, the correct answer is option A) Increasing.

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The new amount due, subtract the discount of $52.57 from the original bill of $2,628.53, giving the new amount due of $2,579.06. Therefore, if you pay the bill within 15 days, you will receive a 2% reduction and your bill will be $2,579.06.

To calculate the amount due if paying within 15 days, you would need to apply the 2% discount to the original amount. To do this, first find the amount of the discount by multiplying the original bill of $2,628.53 by 0.02. This gives a discount of $52.57. To calculate the new amount due, subtract the discount of $52.57 from the original bill of $2,628.53, giving the new amount due of $2,579.06. Therefore, if you pay the bill within 15 days, you will receive a 2% reduction and your bill will be $2,579.06.

Original Bill : $2,628.53

Discount (2%) : $2,628.53 x 0.02 = $52.57

Amount Due (after 15 days) : $2,628.53 - $52.57 = $2,579.06

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Thus, Jamie is wrong. In contrast to Bus C, Bus B has less unoccupied seats as a percentage of total seats.

% is a relative number that is used to represent hundredths of the any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage.

Find the complete seating capacity in Bus A first:

Bus A has 28% of the available seats, making its seat count 0.28 x 250 = 70.

Secondly, we can construct an equation system using the number of seats in Bus B compared to Bus C:

The number of seats aboard Bus B will be x.

In that case, Bus C's seating capacity is (2/3)x.

Using the information that there are 250 seats overall, we can find x:

70 (from Bus A) + x (from Bus B) + (2/3)x (from Bus C) = 250

When we simplify this equation, we obtain: (5/3)x = 180

When we solve for x, we get x = 108.

Bus C has (2/3)x = 72 seats, but Bus B has 108 seats.

We can now determine the proportion of vacant seats for each bus:

Out of a total of 108 seats, 38 seats on Bus B are vacant, making the percentage of vacant seats in Bus B (38/108) x 100% = 35.19%.

Out of a total of 72 seats, there are 26 empty seats on Bus C, making the percentage for empty seats there (26/72) x 100% = 36.11%.

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Answer:

what paper is this for this question

Finding the volume of a figure is a useful tool for solving practical problems that involve 3D space and quantities, such as capacity, mass, or density.

Finding the volume of a figure is a common mathematical calculation used in various fields, such as architecture, engineering, physics, and chemistry. The volume of a figure is a measure of the amount of space that it occupies in three-dimensional (3D) space, such as a cube, a cylinder, a sphere, or a complex shape.

One example of a question that can be answered by finding the volume of a figure is "How much water can a swimming pool hold?" The swimming pool is a 3D figure that can be approximated as a rectangular prism, with a length, width, and depth. By multiplying these three dimensions, we can find the volume of the swimming pool, which represents the amount of water it can hold. This information is useful for designing and constructing the swimming pool, as well as for filling and maintaining it.

Another example is "How much concrete is needed to build a retaining wall?" The retaining wall is a 3D figure that can be approximated as a trapezoidal prism, with a length, height, and thickness. By multiplying these three dimensions, we can find the volume of the retaining wall, which represents the amount of concrete required. This information is useful for estimating the cost and resources needed for the project.

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Answer:

-7.9,   -7.881,   -7.88,   0.07,   7.03

Step-by-step explanation:

Numbers provided: 0.07, -7.88, -7.9, 7.03, -7.881

Edmund spent $63.50 on toys and $28 on new clothes, for a total cost of $91.50.

Edmund had $140 and he decided to spend some of that money on toys and some on new clothes. To calculate how much he spent altogether, we need to first figure out how much he spent on each item. For toys, he spent 3/7 of his total money, which is equal to $63.50. For new clothes, he spent 1/5 of his total money, which is equal to $28. Now that we know how much he spent on each item, we can add these two numbers together to figure out how much he spent altogether. When we add $63.50 and $28, we get a total of $91.50. This means that Edmund spent $91.50 on toys and new clothes altogether.

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The measure of angle H is given as 67.5 degrees

The measure for angle I is 112.5 degrees

The question tells us that ∠F must be 67.5°

from the sign, the angles H and the angle F are vertical angles.

Hence the value of ∠F = ∠H

∠H = 67.5°

From the transversal, we can see that the angle E and angle I are corresponding angles

to get angle E

= 67.5° + ∠E = 180 (angles on a straight line)

∠E = 180 - 67.5

∠E = 112.5 degrees

Since ∠E and ∠I are corresponding angles, ∠I = 112.5 degrees

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The stop sign is a regular octagon, so the measure of ∠F must be 67.5°. What is the measure of angle H? Explain what is the measure of angle i ? explain

The z-scores for which 50% of the distribution's area lies between -z and z are: z = -0.675 and z = 0.675.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The normal distribution is symmetric, meaning that the middle 50% of the scores is given between these following percentiles:

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Answer:

d all differet grreek letters

Answer: 2.2

Step-by-step explanation:

Answer:

B) The mean increases by 2.4 because the mean is 1149 and there 6 outliers.

"1. The end behavior of the function f(x) = -x³ + 2x³ -x+4 can be determined by looking at the highest degree term, which is 2x³. Since this term is positive and has an even degree, the end behavior of the function will be the same on both ends. As x approaches negative infinity, the function will approach negative infinity, and as x approaches positive infinity, the function will approach positive infinity. Therefore, the graph of the function will have two arms pointing upwards.

2. The function f(x) = x² -x² -x -1 can also be analyzed by looking at the highest degree term, which is x². However, since the first two terms cancel each other out, we can simplify the function to f(x) = -x -1. As x approaches negative infinity, the function will approach negative infinity, and as x approaches positive infinity, the function will approach negative infinity as well. Therefore, the graph of the function will have a single arm pointing downwards." (ChatGPT, 2023)

The overall area of the exclamation point at the Little Havana billboard is about 24 square ft while rounded to the nearest square foot.

To discover the total area of the exclamation point, we need to calculate the area of the sector and the area of the circle, after which add them collectively.

First, let's find the area of the sector. The formula for the area of a circle area is:

Area of sector = (angle/360) x π x radius^2

Substituting the given values, we get:

Area of sector = [tex](24/360) x π x 9^2 = 16.62 ft²[/tex]

Next, let's find the area of the circle. The components for the area of a circle is:

Area of circle = π x radius^2

Substituting the given value, we get:

Area of circle [tex]= π x 1.5^2 = 7.07 ft²[/tex]

Now, we are able to add the areas of the sector and the circle to get the whole area of the exclamation point:

[tex]6.62 feet² + 7.07 feet² = 23.69 ft²[/tex]

Therefore, the overall area of the exclamation point at the Little Havana billboard is about 24 square ft while rounded to the nearest square foot.

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Given the ASA postulate, it is seen that ABC and DEF are congruent

The ASA congruence theorem is a postulate in Euclidean geometry that states that if two angles and the side between them in one triangle are congruent to the corresponding angles and sides in another triangle, then the two triangles are congruent.

More formally, the statement of the ASA congruence theorem can be summarized as follows:

If in two triangles, two pairs of corresponding angles are congruent, and the included sides are also congruent, then the triangles are congruent.

angles ABC and DEF are congruent because they have the same size and shape.

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By De Moivre's formula, the square roots of the complex number √(i 2) are √z = 1 + i and √z = - 1 - i, respectively.

In this problem we find a complex number, whose square roots can be determined by De Moivre's formula:

For z = a + i b:

√z = √r · [cos [(θ + 2π · k) / 2] + i sin [(θ + 2π · k) / 2]], for k = {0, 1}

Where:

If we know that r = 2 and θ = π / 2, then the root of the complex number is:

k = 0

√z = √2 · [cos (π / 4) + i sin (π / 4)]

√z = 1 + i

k = 1

√z = √2 · [cos (5π / 4) + i sin (5π / 4)]

√z = - 1 - i

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Answer:

To compare the deals, we need to find the price per milliliter of lemonade for each deal.

For the first deal, the price per milliliter is:

94p / 500ml = 0.188p/ml

For the second deal, the price per milliliter is:

£1.44 / 750ml = 0.192p/ml

Therefore, the first deal is better as it has a lower price per milliliter of lemonade.